A094091 a(1) = 0; for n>0, a(n) = smaller of 0 and 1 such that we avoid the property that, for some i and j in the range S = 2 <= i < j <= n/2, a(i) ... a(2i) is a subsequence of a(j) ... a(2j).

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0

Offset

1,1

Comments

A greedy version of A093383 and A093384.

This is a finite sequence of length 23 (necessarily <= A093382(2) = 31).

For S >= 1 define a sequence by a(1) = 0; for n>0, a(n) = smaller of 0 and 1 such that we avoid the property that, for some i and j in the range S <= i < j <= n/2, a(i) ... a(2i) is a subsequence of a(j) ... a(2j). The present sequence is the case S=2. For S=1 we get a sequence of length 3, namely 0,0,0, and A096094, A106197 are the cases S=3 and S=4. A093382(S) gives an upper bound on their lengths.

Links

Table of n, a(n) for n=1..23.

H. M. Friedman, Long finite sequences, J. Comb. Theory, A 95 (2001), 102-144.

Example

After a(1) = a(2) = a(3) = a(4) = 0 we must have a(5) = 1, or else we would have a(2)a(3)a(4) = 000 as a subsequence of a(3)a(4)a(5)a(6) = 000a(6).

Crossrefs

Cf. A093382, A093383, A093384, A096094, A106197.

Sequence in context: A080343 A011664 A179831 * A080679 A353464 A144193

Adjacent sequences: A094088 A094089 A094090 * A094092 A094093 A094094

Keyword

nonn,fini,full,easy

Author

N. J. A. Sloane, May 02 2004

Extensions

The remaining terms, a(17)-a(23), were sent by Joshua Zucker, Jul 23 2006

Status

approved